Related papers: Particle filtering methods for partially observed …
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…
We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Event-based sampling has been proposed as a general technique for lowering the average communication rate in remote state estimation, which can be important in scenarios with constraints on resources such as network bandwidth or sensor…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…
Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
This article introduces estimators of trend and seasonality for time series of point processes. We assume the point processes follow a temporal or spatial doubly-stochastic Poisson model with log-Gaussian intensity functions. The proposed…